QuestionCalculate the value of $3 - [3 + (3 \cdot 2 + 6)] \div 3$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $3-[3+(3 \cdot+6)] \div3$ . We need to simplify this expression3. We will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is often abbreviated as PEMAS.

STEP 2

First, we need to simplify the expression inside the parentheses.
$\cdot2+6$

STEP 3

Perform the multiplication operation first, as per the order of operations.
$3 \cdot2 =6$ So, the expression becomes $6+6$

STEP 4

Now, perform the addition operation.
$6+6 =12$

STEP 5

Replace the value we just calculated back into the original expression. The expression now becomes $3-[3+12] \div3$

STEP 6

Next, we need to simplify the expression inside the square brackets.
$3+12$

STEP 7

Perform the addition operation.
$3+12 =15$

STEP 8

Replace the value we just calculated back into the original expression. The expression now becomes $3-15 \div3$

STEP 9

Next, we need to perform the division operation, as per the order of operations.
$15 \div3$

STEP 10

Perform the division operation.
$15 \div3 =5$

STEP 11

Replace the value we just calculated back into the original expression. The expression now becomes $3-5$

STEP 12

Finally, perform the subtraction operation.
$-5 = -2$ The solution to the given expression is -2.

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QuestionCalculate the value of $3 - [3 + (3 \cdot 2 + 6)] \div 3$ .

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the parentheses.
$\cdot2+6$

STEP 3

Perform the multiplication operation first, as per the order of operations.
$3 \cdot2 =6$ So, the expression becomes $6+6$

STEP 4

Now, perform the addition operation.
$6+6 =12$

STEP 5

Replace the value we just calculated back into the original expression. The expression now becomes $3-[3+12] \div3$

STEP 6

Next, we need to simplify the expression inside the square brackets.
$3+12$

STEP 7

Perform the addition operation.
$3+12 =15$

STEP 8

Replace the value we just calculated back into the original expression. The expression now becomes $3-15 \div3$

STEP 9

Next, we need to perform the division operation, as per the order of operations.
$15 \div3$

STEP 10

Perform the division operation.
$15 \div3 =5$

STEP 11

Replace the value we just calculated back into the original expression. The expression now becomes $3-5$

STEP 12

Finally, perform the subtraction operation.
$-5 = -2$ The solution to the given expression is -2.

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QuestionCalculate the value of 3−[3+(3⋅2+6)]÷33 - [3 + (3 \cdot 2 + 6)] \div 33−[3+(3⋅2+6)]÷3.

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the parentheses.⋅2+6 \cdot2+6⋅2+6

STEP 3

Perform the multiplication operation first, as per the order of operations.3⋅2=63 \cdot2 =63⋅2=6So, the expression becomes6+66+66+6

STEP 4

Now, perform the addition operation.6+6=126+6 =126+6=12

STEP 5

Replace the value we just calculated back into the original expression. The expression now becomes3−[3+12]÷33-[3+12] \div33−[3+12]÷3

STEP 6

Next, we need to simplify the expression inside the square brackets.3+123+123+12

STEP 7

Perform the addition operation.3+12=153+12 =153+12=15

STEP 8

Replace the value we just calculated back into the original expression. The expression now becomes3−15÷33-15 \div33−15÷3

STEP 9

Next, we need to perform the division operation, as per the order of operations.15÷315 \div315÷3

STEP 10

Perform the division operation.15÷3=515 \div3 =515÷3=5

STEP 11

Replace the value we just calculated back into the original expression. The expression now becomes3−53-53−5

STEP 12

Finally, perform the subtraction operation.−5=−2-5 = -2−5=−2The solution to the given expression is -2.

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QuestionCalculate the value of $3 - [3 + (3 \cdot 2 + 6)] \div 3$ .

First, we need to simplify the expression inside the parentheses.
$\cdot2+6$

Perform the multiplication operation first, as per the order of operations.
$3 \cdot2 =6$ So, the expression becomes $6+6$

Now, perform the addition operation.
$6+6 =12$

Replace the value we just calculated back into the original expression. The expression now becomes $3-[3+12] \div3$

Next, we need to simplify the expression inside the square brackets.
$3+12$

Perform the addition operation.
$3+12 =15$

Replace the value we just calculated back into the original expression. The expression now becomes $3-15 \div3$

Next, we need to perform the division operation, as per the order of operations.
$15 \div3$

Perform the division operation.
$15 \div3 =5$

Replace the value we just calculated back into the original expression. The expression now becomes $3-5$

Finally, perform the subtraction operation.
$-5 = -2$ The solution to the given expression is -2.